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The circular chromatic number of the Mycielskian of G d k
Author(s) -
Huang Lingling,
Chang Gerard J.
Publication year - 1999
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/(sici)1097-0118(199909)32:1<63::aid-jgt6>3.0.co;2-b
Subject(s) - combinatorics , mathematics , chromatic scale , clique number , graph , discrete mathematics
In a search for triangle‐free graphs with arbitrarily large chromatic numbers, Mycielski developed a graph transformation that transforms a graph G into a new graph μ( G ), we now call the Mycielskian of G , which has the same clique number as G and whose chromatic number equals χ( G ) + 1. Chang, Huang, and Zhu [G. J. Chang, L. Huang, & X. Zhu, Discrete Math, to appear] have investigated circular chromatic numbers of Mycielskians for several classes of graphs. In this article, we study circular chromatic numbers of Mycielskians for another class of graphs G d k . The main result is that χ c (μ( G d k )) = χ(μ( G d k )), which settles a problem raised in [G. J. Chang, L. Huang, & X. Zhu, Discrete Math, to appear, and X. Zhu, to appear]. As χ c ( G d k ) = ${k}\over{d}$ and χ( G d k ) =$\lceil {{k}\over{d}} \rceil$ , consequently, there exist graphs G such that χ c ( G ) is as close to χ( G ) − 1 as you want, but χ c (μ( G )) = χ(μ( G )). © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 63–71, 1999